Uncle Sam, the world's largest bill payer, yesterday launched a major overhaul of the way those bills are paid.

Instead of sending checks, the government will make payments by computer, transferring money directly into the bank accounts of thousands of firms with which it does business

Social Security recipients, federal workers and retirees have had the option of getting their monthly checks by direct deposit for a decade.

And some of the largest government contractors have been paid for years by direct deposit as well.

But the new program, which is being run by the Treasury Department's Financial Management Service, has as its goal a complete transfer to a checkless government payment system for businesses.

The first three agencies making the switch yesterday were the Department of Housing and Urban Development, the Education Department and the Health Care Financing Administration.

Initially, only 3,000 payments will be made electronically each month by the three agencies as officials check to ensure that there are no problems in the switchover.

The Labor Department will follow in September and by the end of the year, with other agencies added, the government expects to be making 50,000 business payments a month by computer.

By 1990, the goal is to have switched 50 million of the 77 million business payments the government makes each year to computer transfers.

The reason for the change is simple: money. It costs 26 cents to print and mail out a paper check, but the government estimates sending the payments electronically will cost only 3 cents each.

The Financial Management Service, the agency responsible for paying the bills, expects to save up to $18 million a year when the new system is fully operational.

While Social Security recipients and other individuals will continue to have the option of using direct deposit or getting a monthly check, businesses will not have a choice. If they are dealing with a government agency that has converted to the new "vendor express system," they will be paid by direct deposit.

There are 80,000 firms in the country that make at least $25,000 in sales to the government annually, and officials estimate another 150,000 businesses are paid less than that each year.

FMS Commissioner William E. Douglas said in addition to the amount of the payment, the government is also transmitting electronically an invoice number so that firms will know which bill is being paid.

Douglas said it would be up to each business to work out an arrangement with the bank on notification of when the government payment is received. He said banks are expected to meet business demands or risk losing their accounts.

Douglas said if there are any problems in the new program they will likely show up in the first two months. But Douglas said officials believed they had anticipated most difficulties, drawing on the experience gained with 10 years of making Social Security payments electronically.

"The government was the real pioneer in direct deposit payments," he said. "We expect the new program will make a big impact as well, prompting many medium-sized corporations who haven't been involved in electronic transfers to get involved."

At present, 43 percent of the country's 37 million Social Security recipients receive their benefits by direct deposit.

In all, government payments account for 48 percent of the 750 million electronic payments made each year